\item \lect Use the DPLL algorithm with conflict-driven clause learning to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{negative} phase. For conflicts, draw conflict graphs after the end of the table, and add the learned clause to the table.\\
If the set of clauses resulted in \texttt{SAT}, give a satisfying model. If the set of clauses resulted in \texttt{UNSAT}, give a resolution proof that shows that the conjunction of the clauses from the table is unsatisfiable.

\begin{dpllCNFInput}
    \item $(\lnot a \lor \lnot c)$
    \item $(b \lor c)$
    \item $(\lnot b \lor \lnot d)$
    \item $(\lnot d \lor e)$
    \item $(d \lor e)$
    \item $(a \lor \lnot c \lor \lnot e)$
    \item $(\lnot b \lor c \lor d)$
\end{dpllCNFInput}